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MathGroup Archive 2006

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Re: the ellipse and the circle

  • To: mathgroup at smc.vnet.net
  • Subject: [mg69219] Re: the ellipse and the circle
  • From: Urijah Kaplan <uak at sas.upenn.edu>
  • Date: Sun, 3 Sep 2006 01:39:02 -0400 (EDT)
  • Organization: University of Pennsylvania
  • References: <200609011041.GAA25668@smc.vnet.net> <edadmf$pef$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

After using those options, try using FullSimplify[Reduce[]] instead of 
Solve[] on your equations, and see if you like the form of those answers.

           --Urijah

> 
> Your equations are equivalent to finding the roots of a 4th order 
> polynomial. By default, Solve will use radicals to express the root of a 
>   quartic polynomial, and hence yields an enormous and useless result in 
> this case. We can control this behavior by changing the options of Roots:
> 
> SetOptions[Roots, Cubics -> False, Quartics -> False]
> 
> Now using Solve will produce much smaller results at the cost of 
> containing explicit Root objects.
> 
> Carl Woll
> Wolfram Research
> 
>> In[1]:=
>> $Version
>> Out[1]=
>> "5.1 for Microsoft Windows (October 25, 2004)"
>> In[3]:=
>> e = x^2/a^2 + y^2/b^2 == 1
>> Out[3]=
>> x^2/a^2 + y^2/b^2 == 1
>> In[4]:=
>> x0 = a*Cos[\[Theta]]
>> Out[4]=
>> a*Cos[\[Theta]]
>> In[5]:=
>> y0 = b*Sin[\[Theta]]
>> Out[5]=
>> b*Sin[\[Theta]]
>> In[6]:=
>> c = (x - x0)^2 + (y - y0)^2 == r^2
>> Out[6]=
>> (x - a*Cos[\[Theta]])^2 + (y - b*Sin[\[Theta]])^2 == r^2
>> In[7]:=
>> Solve[{e, c}, {x, y}]
>>
>> [thousand of lines deleted]
> 


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